Mixing and transport in dendritic mitochondria

Neurons contain long, branched projections (axons and dendrites) whose distal tips play an important role in cell growth and signal transmission, requiring high rates of energy consumption. Mitochondria are localized throughout these projections in order to supply energy and buffer calcium levels. These dynamic organelles undergo continuous fusion and fission events, facilitating the delivery of newly synthesized proteins and the homogenization of mitochondrial contents. Our work focuses on the mathematical modeling of mixing through mitochondrial populations in complex neural geometries. We use a combination of agent-based simulations and mean-field modeling to probe the key physical features that govern the dispersion and turnover of mitochondrial material in dendritic trees. Our results demonstrate that the spreading of mitochondrial contents depends on a few key parameters - the turnover timescale, the number of stopping events, and the average cluster size in the population of mitochondria. Model predictions are compared against experimental data quantifying the dynamics of photoconverted mitochondrial protein in Drosophila sensory dendrites, with and without perturbed expression of the mitochondrial fusion factor Marf. Marf overexpression is observed to enhance protein dispersion without substantially altering the mitochondrial transport flux, consistent with a model that incorporates upregulated transient kiss-and-run fusion events. Overall, mixing in the mitochondrial population is found to be governed by a complex interplay of directed transport and interactions between individual organelles.